RESEARCH ARTICLE

Flight mechanics and control of escape manoeuvres inhummingbirds. I. Flight kinematicsBoCheng1,*, BretW. Tobalske2, Donald R. Powers3, Tyson L. Hedrick4, SusanM.Wethington5, George T. C. Chiu6

and Xinyan Deng6

ABSTRACTHummingbirds are nature’s masters of aerobatic manoeuvres.Previous research shows that hummingbirds and insects convergedevolutionarily upon similar aerodynamic mechanisms and kinematicsin hovering. Herein, we use three-dimensional kinematic data to beginto test for similar convergence of kinematics used for escape flightand to explore the effects of body size uponmanoeuvring.We studiedfour hummingbird species in North America including two largespecies (magnificent hummingbird, Eugenes fulgens, 7.8 g, andblue-throated hummingbird, Lampornis clemenciae, 8.0 g) and twosmaller species (broad-billed hummingbird, Cynanthus latirostris,3.4 g, and black-chinned hummingbirds Archilochus alexandri,3.1 g). Starting from a steady hover, hummingbirds consistentlymanoeuvred away from perceived threats using a drastic escaperesponse that featured body pitch and roll rotations coupled with alarge linear acceleration. Hummingbirds changed their flappingfrequency and wing trajectory in all three degrees of freedom on astroke-by-stroke basis, likely causing rapid and significant alterationof the magnitude and direction of aerodynamic forces. Thus itappears that the flight control of hummingbirds does not obey the‘helicopter model’ that is valid for similar escape manoeuvres in fruitflies. Except for broad-billed hummingbirds, the hummingbirds hadfaster reaction times than those reported for visual feedback control ininsects. The two larger hummingbird species performed pitchrotations and global-yaw turns with considerably larger magnitudethan the smaller species, but roll rates and cumulative roll angles weresimilar among the four species.

KEY WORDS: Hummingbird, Escape, Flapping, Pitch, Roll

INTRODUCTIONHummingbirds and many flying insects are capable of sustainedhovering and performing a suite of remarkably fast aerobaticmanoeuvres. These species use high-frequency and high-angle-of-attack wing motions during hovering (Dudley, 2000; Ellington,1984). This is distinct from the flight of conventional human-engineered aircraft with fixed (Anderson, 2005) or rotary wings(Leishman, 2006) or the forward, cruising flight of most bird species

(Tobalske et al., 2003). Previous research has shown thathummingbirds have converged evolutionarily with insects uponaerodynamic mechanisms and wing kinematics used in steadyhovering (Warrick et al., 2005, 2009), but insight is lacking into howhummingbirds use their wings to accomplish high-intensitymanoeuvres.

The flapping motions used by hummingbirds and insects, withaerodynamic force production during most of wingbeat cycle(Warrick et al., 2009), should facilitate authority of flight controlbecause it allows for rapid and drastic alterations to the magnitudeand direction of flight forces to the extent that the animal can alter itswing kinematics (Read et al., 2016). However, closed-loop controlof flapping flight during maximal manoeuvres may imposestringent demands on neural-sensing and motor-control systems.Latencies in sensorimotor transduction (Chang and Wang, 2014;Elzinga et al., 2012; Ristroph et al., 2013) and maximal power offlight muscle (Ellington, 1985; Josephson et al., 2000) couldsignificantly limit manoeuvrability. In this respect, hummingbirdsmay be better than insects at leveraging locomotive advantagesoffered by a flapping wing using their more elaborate neural andphysiological systems. Hummingbird flight muscles have someanaerobic capacity (Chai and Dudley, 1996), which may allow themto generate significantly higher mass-specific power than insectsduring burst flight (Chai et al., 1997; Marden, 1994), theirskeletomuscular system (Hedrick et al., 2011; Welch andAltshuler, 2009) may provide more degrees of freedom of wingmotion to facilitate large changes of manoeuvring forces andmoments, and their nervous system has higher computational powercompared with insects (Iwaniuk and Wylie, 2007), and, therefore,may offer more-complex, high-level flight control throughprediction and planning (Flanagan and Wing, 1997; Mischiatiet al., 2015).

Therefore, the flight control of hummingbirds, especially duringmanoeuvres with near-maximal performance, may represent anideal example for assessing the locomotive advantages offeredby flapping flight. Understanding the manoeuvrability ofhummingbirds in relation to complex interactions between thephysics of flight and neural sensing and motor systems could lead tosignificant progress in broader animal-locomotion theory, and couldalso be valuable for biomimetic design of micro air vehicles usingflapping wings (Keennon et al., 2012; Ma et al., 2013; Roll et al.,2015).

Considerable research on hummingbird flight has focused onmaximal performance during load-lifting (Chai and Dudley, 1995;Chai and Millard, 1997; Altshuler et al., 2010) and during sexuallyselected displays (Clark, 2009, 2011), but these studies have notincluded detailed analyses of wing motion that would be usefulfor improving understanding of underlying flight mechanicsand control. Within the repertoire of aerobatic manoeuvres ofhummingbirds, we chose to study escape manoeuvring from aReceived 18 January 2016; Accepted 25 August 2016

1Department of Mechanical and Nuclear Engineering, Pennsylvania StateUniversity, University Park, PA 16802, USA. 2Field Research Station at FortMissoula, Division of Biological Sciences, University of Montana, Missoula, MT59812, USA. 3Biology & Chemistry Department, George Fox University, Newberg,OR 97132, USA. 4Department of Biology, University of North Carolina, Chapel Hill,NC 27599, USA. 5Hummingbird Monitoring Network, PO Box 115, Patagonia,AZ 85624, USA. 6School of Mechanical Engineering, Purdue University, WestLafayette, IN 47907, USA.

*Author for correspondence (buc10@psu.edu)

B.C., 0000-0002-6982-0811

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hovering start because: (1) it is characterized by rapid and large-angle rotations about all three body axes (Clark, 2011) and,therefore, should pose significant challenges in flight control andstabilization, a central problem for both natural and human-madeflapping-wing fliers; (2) it is an ecologically relevant behaviourwhich hummingbirds are able to perform from start to finish evenin a confined space, and is therefore amenable to laboratorystudies; and (3) only minor stimuli are necessary to repeatedlyelicit escape manoeuvres from vigilant hummingbirds andhypothetically the associated flight performance could be nearmaximal.With the goal of improving the understanding of mechanics and

control (see companion paper, Cheng et al., 2016), herein we reporton the free-flight body and wing kinematics of hummingbirds,during escape from a perceived threat in which their manoeuvringflight performance should be close to maximal (Jackson and Dial,2011). We hypothesize that hummingbirds take advantage oftheir jointed wing-skeleton to produce larger deviations in wingkinematics than those used by insects during startle or loomingavoidance manoeuvres, allowing for multi-axis acrobaticmanoeuvres. Additionally, we test the effects of body size onmanoeuvring performance. Mass-specific power available for load-lifting appears to be invariant with body mass (Altshuler et al.,2004), and this empirical evidence leads to the prediction thatcapacity for manoeuvring should scale similarly. In contrast, scalingtheory (Kumar and Michael, 2012) suggests that smaller speciesshould manoeuvre more easily than larger species so that largerspecies may require larger wing kinematic changes to achievesimilar levels of performance (this has been discussed in acompanion paper, Cheng et al., 2016). We address thesequestions here using detailed examination of the kinematics of

escape manoeuvres of four species of hummingbirds that vary inbody mass and wing and tail morphology.

MATERIALS AND METHODSBird capture and housingWe studied four hummingbird species in North America (N=2males per species; Table 1) including two large species, magnificent[Eugenes fulgens (Swainson 1827), 7.5 and 8.0 g] and blue-throatedhummingbirds [Lampornis clemenciae (Lesson 1829), 7.8 and8.1 g], and two smaller species, broad-billed (Cynanthus latirostrisSwainson 1827, 3.3 and 3.4 g) and black-chinned hummingbirds[Archilochus alexandri (Bourcier &Mulsant 1846), 3.1 g]. Captureand experimentation with magnificent and blue-throatedhummingbirds occurred at Southwestern Research Station,American Museum of Natural History, Portal, Arizona, USA(altitude 1450 m), and with broad-billed and black-chinnedhummingbirds in Patagonia, Arizona, USA (altitude 1236 m).Birds were captured using modified Russell traps (Russell andRussell, 2001) with soft mesh, and they were housed individually in1×1×1 m flight cages with nutrition available ad libitum in the formof Nektar Plus (NEKTON® Günter Enderle, Pforzheim, Baden-Württemberg, Germany) and a 20% sucrose solution (mass:volume). Capture and housing were permitted by the US Fish andWildlife Service and the Arizona Game and Fish Department. Birdswere released unharmed after 3–5 days in captivity. Animalprocedures were approved by the Institutional Animal Care andUse Committees of the University of Montana and PurdueUniversity.

We obtained morphometrics from the animals using standardtechniques (Tobalske et al., 1999) immediately after theexperiments. We measured body mass (m) using a digital balancewith a resolution of 0.01 g. We photographed the animals ventral-side down with one wing spread as in mid-downstroke and also ontheir back, wings folded and with the head relaxed but the beakgently restrained to be in line with the long axis of the body. Thelengths of the beak and tail were included in the body lengthmeasurements. Note that flexible body segments and feathersintroduce some uncertainty.

Experiment setup and protocolWe conducted experiments with the hummingbirds inside atransparent flight chamber (87×77×61 cm) made of acrylic plasticwith an open-mesh floor and an elevated perch (Fig. 1A). Forfeeding during the experiments, we used a modified 3-ml plasticsyringe (1 cm in cross-sectional diameter) filled with 20% sucrosesolution. The feeder was suspended approximately 22 cm from thetop and next to one side of the chamber. Birds were introduced to thechamber individually after habituation to captivity (indicated bycalm perching in their housing cage). The experiments started afterthe birds demonstrated voluntary, relaxed feeding in the chamber.During the experiments, we monitored for undue stress or abnormalbehaviour; if instances were observed, the birds were returned totheir housing.

To elicit near-maximal escape performance, escape from steadyhovering to another position in the chamber in minimum time,one investigator startled each feeding bird using a 23×31 cmblack clipboard, held outside the chamber 1 m from the bird. Theinvestigator held the clipboard adducted, perpendicular to the floor,broad side facing the hummingbird. The investigator used bothhands to thrust the clipboard horizontally toward the hoveringhummingbird. A single investigator produced all startle stimuli in aneffort to minimize variance in presentation among trials. After

List of symbols and abbreviationsAR aspect ratioLbody body lengthLculmen culmen lengthLtail tail lengthm body massn wingbeat frequency(p, q, r) body roll, pitch and yaw angular velocityR wing lengthr dimensionless wing spanwise locationr2(S) dimensionless radius of second moment of wing areaRe Reynolds numbert dimensionless timet0 start time of the escape manoeuvre (time instant of tail

flaring)tf end time of the escape manoeuvretr start time of the roll rotation(u, v, w) body linear velocities along the principal axesUl stroke-averaged left wing tip velocityUr stroke-averaged right wing tip velocityUw stroke-averaged wing tip velocity at hover(X, Y, Z ) global coordinate frame(xb, yb, zb) body coordinate frame(xs, ys, zs) horizontal stroke plane coordinate frame(xw, yw, zw) wing coordinate frameγ stroke plane angleθ wing stroke deviation angleφ stroke position angleΦ wingbeat amplitudeψ wing rotation angleψ0 wing rotation angle at wing baseψtw wing twist rate

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preliminary experiments, this type of startling stimuli was chosen asit was the most effective in generating repeatable, vigorous escape.Previous startle experiments using streamertail hummingbirds

(Trochilus polytmus) (Clark, 2011) found that the presence of theexperimenter significantly increased the vigilance of all the birds,and therefore increased the likelihood of maximal performance in

Table 1. Morphometrics of the four hummingbird species studied

Species Subjects m (g) Lbody (mm) R (mm) AR r2(S) R/Lbody Ltail/Lbody Lculmen/Lbody

R3/m(104 mm3 g−1)

Blue-throated (Lampornis clemenciae) 1 7.82 129.93 78.90 7.78 0.50 0.61 0.31 0.18 6.282 8.09 121.43 76.40 7.30 0.51 0.63 0.32 0.19 5.51Mean 7.96 125.68 77.65 7.54 0.50 0.62 0.31 0.18 5.90s.d. 0.19 6.01 1.77 0.34 0.00 0.02 0.00 0.01 0.54

Magnificent (Eugenes fulgens) 1 7.49 124.72 72.60 7.53 0.50 0.58 0.31 0.21 5.112 7.96 122.59 76.80 7.86 0.49 0.63 0.32 0.23 5.69Mean 7.73 123.66 74.70 7.70 0.49 0.60 0.32 0.22 5.40s.d. 0.33 1.51 2.97 0.24 0.00 0.03 0.01 0.01 0.41

Black-chinned (Archilochus alexandri) 1 3.09 79.95 46.30 8.15 0.48 0.58 0.29 0.23 3.212 3.13 78.47 46.80 7.19 0.50 0.60 0.29 0.24 3.27Mean 3.11 79.21 46.55 7.67 0.49 0.59 0.29 0.23 3.24s.d. 0.03 1.05 0.35 0.68 0.01 0.01 0.00 0.00 0.04

Broad-billed (Cynanthus latirostris) 1 3.37 94.12 53.70 7.63 0.49 0.57 0.29 0.22 4.602 3.32 91.54 57.10 7.59 0.50 0.62 0.28 0.25 5.61Mean 3.35 92.83 55.40 7.61 0.50 0.60 0.29 0.24 5.10s.d. 0.04 1.82 2.40 0.03 0.01 0.04 0.00 0.02 0.72

See the List of symbols and abbreviations for definitions of variables. Values of R3/m are shown to illustrate the scaling of wing length relative to body mass; alarger R3/m indicates a relatively longer wing span or smaller body mass.

CAM3

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Fig. 1. Experiment setup and definition of kinematics. (A) Experiments were conducted in a flight chamber with an open-mesh floor. Prior to startle, astationary hovering hummingbird is feeding on a feeder modified from a plastic syringe. The startling stimulus generated by the impulsive movement of a blackclipboard elicited the escape manoeuvre. Three synchronized high-speed video cameras were used to record the entire course of the manoeuvre. The globalcoordinate frame is defined along fore/aft (X ), lateral (Y ) and vertical (Z ) directions. (B) Anatomical landmarks (blue filled dots) used for the extraction ofkinematics were located on the head, body, wings and tail of the bird. (C) Details of the anatomical landmarks on the wing show their locations on the primary andsecondary feathers and the definitions of proximal and distal planes used for the extraction of wing kinematics. (D) Illustration of body (xb, yb, zb), horizontal strokeplane (xs, ys, zs) and wing (xw, yw, zw) coordinate frames. The wing stroke (φ), deviation (θ) and rotation (ψ) angles are defined with respect to the horizontal strokeplane frame. The body linear and angular velocities are specified by (u, v, w) and (p, q, r), respectively.

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escape. No training of the birds for the escape manoeuvres wasrequired. Habituation was not apparent: each bird in a singleexperiment period was repeatedly startled at least five times, andamong these trials no significant order effect was observed. Fivetrials were recorded on video for each bird, and two of these trialswere analyzed quantitatively, giving N=4 quantitative samples ofkinematics per species.In separate trials, the startling stimuli were sent to the birds from

either frontal or lateral directions. While only the escapemanoeuvres from the frontal startles were analyzed quantitativelyin this study, qualitative results from the lateral startles were used toexplore whether the birds used other distinct manoeuvring patterns.

High-speed videography and kinematics extractionWe used three synchronized high-speed video cameras, one SA3and two PCI-1024 (1024×1024 pixel resolution) (Photron Inc., SanDiego, CA, USA), sampling at 1000 frames s–1 and with a shutterspeed of 1/6000 s (for magnificent and blue-throatedhummingbirds) and 1/10,000 s (for black-chinned and broad-billed hummingbirds). We illuminated the chamber from outsideusing four 650-W halogen lights (Lowel Tota-light, Lowel-LightManufacturing, Brooklyn, NY, USA) and two 50-W LED lights(Fancier LED500, Ningbo Fancier Photographic Equipment Co.,Zhenhai, Ningbo, China).Cameras were calibrated using a direct linear transformation for

three-dimensional kinematic reconstruction (Hedrick, 2008). Wedigitized anatomical landmarks (Fig. 1B) using DLTdv5(Hedrick, 2008). We marked the birds prior to the experimentsusing 1.5-mm dots of non-toxic, water-soluble white paint. Weplaced five markers on each wing (Fig. 1C). In kinematicanalyses, proximal and distal wing planes were defined usingposition vectors based on these points. We placed markers on thelateral tail feathers (Fig. 1B), and defined tail-flaring angle usingthese points. Head orientation was determined treating the eyesand base of the culmen as points on a plane. Body location wasdetermined as the centroid of markers placed on the feathers overthe mid-thoracic spine and each lateral tail junction with the body.The body principal-roll axis (xb) was determined using the vectorfrom the averaged location of lateral tail–body junctions to themarker on the spine; pitch axis (yb) by averaging two lateralvectors (one connecting lateral tail–body junctions and the otherconnecting two wing bases); and yaw axis (zb) by the cross-product of the roll and pitch axes (Fig. 1B,D). Horizontal strokeplane frame (xs, ys, zs) was defined by rotating the body frame byan angle equal to the hovering pitch angle.Body roll, pitch and yaw Euler angles (using the Fick convention,

Murray et al., 1994) were calculated using a rotation matrix fromglobal frame (X, Y, Z) to body frame. Body angular velocities abouteach principal axis were calculated using the derivative of therotation matrix (Murray et al., 1994). Time series of bodykinematics were low-pass filtered with a cut-off frequency of twotimes (revealing the within-wingbeat oscillation) or half (no within-wingbeat oscillation) of flapping frequency. Reaction time wascalculated as the difference between the start of stimulus (when theclipboard started to move) and tail flaring (e.g. Fig. S1).

Kinematic model of flapping wingsCoordinate frames rooted at the wings (xw, yw, zw) were definedaccording to Fig. 1D. Two sets of wing kinematics, distal andproximal, were obtained using the Euler angles (stroke position φ,stroke deviation θ and wing rotation ψ) derived from the rotationmatrices from the horizontal stroke plane frame to the distal and

proximal wing planes (Fig. 1C,D), respectively. Time series of wingEuler angles were obtained for each trial including the entire periodof the manoeuvre and at least three hovering wingbeat cycles priorto manoeuvre. A hovering wing kinematic pattern for each specieswas obtained by averaging hovering kinematics from four trials.During analysis, we found that the largest changes of wingkinematic angles were coincident with peak angular velocities ofthe body. Therefore, nominal manoeuvring wing kinematic patternsfor generating pitching and rolling moments were obtained for eachspecies by averaging the wingbeat cycles corresponding to peakangular velocities from four trials within a species.

Euler angles of identified wing kinematic patterns wereparameterized using a third-order Fourier series prior to furtheranalysis:

fðtÞ ¼ f0 þX3

i¼1

fsi sinð2pitÞ þ fci cosð2pitÞ; ð1Þ

uðtÞ ¼ u0 þX3

i¼1

usi sinð2pitÞ þ uci cosð2pitÞ; ð2Þ

ck ðtÞ ¼ c0;k þX3

i¼1

csi;k sinð2pitÞ þ cci;k cosð2pitÞ; ð3Þ

where t is dimensionless time (varying from 0 to 1 in a wing strokecycle); k indicates wing rotation angle derived from distal (k=d ) orproximal (k=p) planes; and ψ0, θsi, ψsi,k, etc. are coefficients of theharmonics, which were selected to yield the best least-squares fit tothe wing kinematic Euler angles (see Fig. S2 for an example oforiginal data).

Owing to substantial spanwise twist, the distal and proximal wingplanes had significantly different wing rotation angles but similarstroke position and deviation angles. To quantify wing twist forblade-element analysis (Cheng et al., 2016), we assumed that allwing chord sections shared the same stroke and derivation angleswhile having a linearly varying rotation angle from wing base to tip(e.g. a linear twist model; Leishman, 2006; Walker et al., 2009),where local rotation angle of a wing chord section is a linearfunction of dimensionless spanwise location r (0 � r � 1, where 0represents the wing base and 1 represents the wing tip):

cðr; tÞ ¼ c0ðtÞ þ rctwðtÞ; ð4Þwhere ψ0 is wing rotation angle at wing base and ψtw is wing twistrate. Both ψ0 and ψtw are also parameterized by the third-orderFourier series, as they are time-varying functions determined by therotation angles of proximal and distal wing planes, ψd(t) and ψp(t):

ctwðtÞ ¼cdðtÞ � cpðtÞ

rd � rp

¼ c0;tw þX3

i¼1

csi;tw cosð2pitÞ þ cci;tw sinð2pitÞ; ð5Þ

c0ðtÞ ¼�cdðtÞrp þ cpðtÞrd

rd � rp

¼ c0;0 þX3

i¼1

csi;0 cosð2pitÞ þ cci;0 sinð2pitÞ; ð6Þ

where rd and rp are the dimensionless spanwise locations ofdistal and proximal wing planes, respectively, estimated from thecentroids of the corresponding wing planes. We assumed whenhummingbirds changed their wing rotation angle during the

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manoeuvres, ψ0 remained constant and only ψtw changedaccording to:

ctw;manoeuvreðtÞ ¼cd;manoeuvreðtÞ � c0ðtÞ

rd: ð7Þ

Statistical analysis of manoeuvring kinematicsWe performed statistical analyses to assess the relationshipsbetween changes in wing kinematic patterns and resulting bodymovements. We computed mean values of wing kinematicvariables, including: stroke, deviation, wing rotation, angle ofattack, magnitude of wing-tip velocity, stroke–plane angle andflapping frequency. For kinematic variables of the body, wecalculated mean linear and angular velocities and accelerations overthe interval of 0.15 s from the start of the manoeuvre, which wastime interval of the manoeuvres of shortest duration. Means werecomputed over the upstrokes and downstrokes separately. For wingkinematic variables, they were based on both bilateral symmetricand asymmetric changes. Hypothetically, bilateral–symmetricchanges were used for generating longitudinal body movements(i.e. pitch rotation and fore/aft and vertical translation) and bilateral–asymmetric changes were used for generating lateral bodymovements (i.e. roll and yaw rotation and lateral translation). Wecomputed Pearson’s linear correlation coefficients and P-values(double-tailed Student’s t-distribution) between each pair of wingand body kinematic variables using MATLAB (The MathWorks,Natick, MA, USA).

RESULTSMorphometrics and scalingOur sampling of only four species precluded formal statisticalanalysis of scaling relationships, so we limit our interpretation togeneral comparisons with broader samples (Greenewalt, 1962). Thefour species exhibited almost identical wing planform (Table 1).The two larger species had slightly higher tail-to-body length ratios(Table 1) (consistent with those found in Clark, 2010), suggesting apotentially more important aerodynamic effect of tail in largerspecies. The black-chinned hummingbirds had relatively wideabdomens and larger body masses than those predicted by isometry,which is evident in their lowest values of R3/m among the species(Table 1).

Wingbeat frequency declined with increasing wing length(Table 2). This was consistent with the broader pattern for insectsand hummingbirds, according to the empirical relationshipnR1.15=3540 mm1.15 s−1 (Greenewalt, 1962); but, again, black-chinned hummingbirds were an exception as they used relativelyhigh wingbeat frequencies for their wing length (nR1.15=4201±106 mm1.15 s−1), presumably to help support their relativelylarge body weights. Stroke amplitudes of black-chinnedhummingbirds (Table 2) were approximately 10 deg less than thoseof the other three species. This may be attributed to the physiologicalconstraint that higher wingbeat frequency requires reduced musclestrain (Hedrick et al., 2011). Black-chinned hummingbirds hadsimilar wing length as hawkmoths (Manduca sexta) (Cheng et al.,2011), but they support approximately 2.2 times the body weight andhave approximately two times the disc loading (body weight dividedby the area swept by wings) using approximately two times thewingbeat frequency. Despite differences in wing lengths andwingbeat frequencies, stroke-averaged wing tip velocities (Uw)from four species were all ∼10 m s−1 (Table 2), indicatingrelatively similar muscle-contraction velocities, but black-chinnedhummingbirds had the highest Uw at ∼12 m s−1.

Body kinematic patterns of escape manoeuvreHummingbirds in each species responded to frontal startlingstimulus by steering away using a stereotyped combination ofpitch-and-roll manoeuvres (Fig. 2). In few exceptions (<5% of totalsamples), birds exhibited pitch and backward manoeuvres withoutchanging their heading. We refer to the former as an escapemanoeuvre to emphasize that the bird attempted to fly away from thethreat by changing its heading and the latter as an avoidancemanoeuvre to emphasize that the bird only attempted to back up toavoid the threat.

Both escape and avoidance manoeuvres began with asimultaneous body pitch-up rotation and backward translation. Inavoidance manoeuvres, a bird pitched up until its body longitudinalaxis was almost aligned with the vertical axis, and then it began topitch down while decelerating from the backward translation. Thepitch-down rotation overshot the hover pitch angle until the bodylongitudinal axis was almost horizontal, then the bird pitched upagain and slowly returned to hover posture. Such a manoeuvringpattern was almost identical to that observed previously in the startleresponses of hawkmoths (M. sexta) (Cheng et al., 2011). However,

Table 2. Characteristics of wing kinematics

Species Subjects n (Hz) Φ (deg) Uw (m s−1) Re nR1.15 (mm1.15 s−1)

Blue-throated (Lampornis clemenciae) 1 25.02 152.68 10.17 13,597 38012 22.99 148.305 9.06 12,139 3366Mean 24.00 150.49 9.61 12,868 3583s.d. 1.43 3.09 0.79 1031 307

Magnificent (Eugenes fulgens) 1 22.73 156.49 8.82 11,079 31382 26.79 154.60 11.00 13,821 3945Mean 24.76 155.54 9.89 12,450 3541s.d. 2.87 1.34 1.54 1939 571

Black-chinned (Archilochus alexandri) 1 50.13 149.94 11.37 8796 41252 51.32 135.69 11.77 9437 4276Mean 50.72 142.82 11.57 9117 4201s.d. 0.84 10.08 0.28 454 106

Broad-billed (Cynanthus latirostris) 1 31.25 152.52 8.86 8015 30502 31.28 151.35 9.43 9048 3276Mean 31.27 151.94 9.15 8532 3163s.d. 0.02 0.83 0.40 730 160

Uw is stroke-averaged wing tip velocity at hover. nR1.15 corresponds to an empirical relation of wingbeat frequency and wing length derived from insects andhummingbirds, nR1.15=3540 (mm1.15 s−1) (Greenewalt, 1962). See List of symbols and abbreviations for definitions of other variables.

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avoidance manoeuvres were observed repeatedly in hawkmoths andwere the only type of manoeuvre observed in response to a loomingstartle stimulus. Because of the small number of avoidancemanoeuvres observed, they were not further analyzed in thepresent study.

Pitch-roll escape manoeuvreDuring escape manoeuvres, a hummingbird reoriented its headingthrough a rapid roll rotation at the second half of the escapemanoeuvre, following pitch-up at the first half. This roll not onlyoriented the bird to the direction of escape, but also led to a smoothtransition from backward flight to forward flight without asignificant loss of linear momentum.At the first half of the escape manoeuvre, in addition to the large

pitch, minor body roll and yaw were also observed as they oriented

the bird to the direction of escape. Concurrent with initial pitch-up,all the birds exhibited a subtle body roll that oriented their dorsumtowards the final direction of escape; this was evidenced by anegative roll angular velocity in the beginning of the manoeuvre(blue curves, Fig. 3D,L). There was also a small positive body yawthat oriented the body longitudinal axis towards the direction ofescape (red curves, Fig. 3D,L). These two kinematic featuresincreased the linear acceleration towards the direction of escape atthe first half of the manoeuvre. This simultaneous roll/yaw bodyrotation was similar to banked yaw turns (Muijres et al., 2015) orroll/yaw turns (Clark, 2011) described previously for insects andhummingbirds. However, in the escape manoeuvres observed inthe present study, they had much smaller magnitude comparedwith pitch rotations at the first half and the roll rotations at thesecond half of the manoeuvres. A perfect sequential pitch-roll and a

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Fig. 2. Sequential tracings of escapemanoeuvres and the corresponding body linear and angular velocities of two hummingbirds. (A–D) Amagnificenthummingbird. (E–H) A broad-billed hummingbird. (A,E) Tracings from the high-speed videos superimposed to reflect the actual spatial locations of the birdsover time. Tracings are numbered from 1 (hover) to 8 (completion of body rotation). (B,F) Same tracings as in A and E but arrayed separately so that the bodypostures of the bird are visible. (C,G) Body linear velocities expressed in the global frame. (D,H) Body roll, pitch and yaw angular velocities. The timings of pitch,backward acceleration, roll and forward flight are indicated by the arrows on the top of each graph.

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simultaneous roll/yaw turn are two extremes of the escapemanoeuvres observed by Clark (2011); most manoeuvres havebody rotations distributed in between. A similar distribution is alsoobserved in escaping fruit flies, as they control the relative amountof roll and pitch to change the escape direction when approachedwith danger (Muijres et al., 2014). In the present study, we foundthat the pitch-roll manoeuvres were more dominant thansimultaneous roll/yaw when the danger was from the front. The

birds performed only a small ‘banked turn’ while simultaneouslypitching up in the first half of the manoeuvre and then rolled back tonormal forward flight/hover postures in the second half of themanoeuvre. Because of the dominance of pitch and roll rotation, weuse the term ‘pitch-roll’.

Stroke-averaged body kinematics showed that global yawturning angle was strongly correlated with cumulative bodypitch angle prior to the start of roll rotation (trt0 q � dt, where q is

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Fig. 3. Body kinematics of four individual escape manoeuvres from two hummingbird species. (A–H) Magnificent hummingbirds. (I–P) Black-chinnedhummingbirds. Kinematics include body position (A,I), body linear velocity expressed in the body frame (B,J), body Euler angle (C,K), body angular velocity (D,L),cumulative body rotation angle (E,M) and head Euler angle relative to the global frame (F,N). (G,H) The longitudinal tilt angle of the aerodynamic force vector,defined as the angle between the normal axis of the horizontal stroke plane zs and the projection of the force vector on the longitudinal plane (Fxz), positivebeing a forward tilt. (H,P) The lateral tilt angle of aerodynamic force vector, which is defined as the angle between force vector (F) and its projection on thelongitudinal plane, positive being left tilt. The aerodynamic force vector is calculated based on the body acceleration and gravity. The thick solid curves representthe averaged traces, thin solid curves represent the individual traces, and the shaded areas indicate ±1 s.d. (N=4). The time series of different manoeuvresare aligned at the start of the manoeuvre, which is defined as the instant of tail flaring, and last for 0.15 s, the interval of the manoeuvres of shortest duration.

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pitch rate, and t0 and tr are the starting times of pitch and roll,respectively; Fig. 4A) as well as with the total cumulative bodypitch angle over the entire period of the manoeuvre (tft0 q � dt, wheretf is the final time of manoeuvre, defined as when the roll anglewas approximately zero at the end of the manoeuvres; Fig. 4B).However, the correlation between the yaw turning angle and thetotal cumulative roll angle (tft0 p � dt), primarily at the second half ofthe manoeuvre, was relatively weak compared with the formervariables (Fig. 4C). Representations of t0, tr and tf are shown inFig. 3E. Because the cumulative body pitch angle prior to the startof the roll rotation reflected the timing of the roll rotation relativeto the pitch rotation (or the pitch angle when the bird started toroll), the birds were able to perform global yaw turns with varyingmagnitude by simply controlling the timing of roll rotation. Forexample (Fig. 2), compare a 180 deg yaw turn performed by amagnificent hummingbird (larger species) with a 140 deg yawturn performed by a broad-billed hummingbird (smaller species).Pitch-roll manoeuvres were also used by all of the species inresponse to lateral-startling stimuli, but in these cases, themanoeuvres had earlier timings of roll rotation compared withthose in response to frontal-startling stimuli, thus leading tosmaller global yaw turns close to 90 deg.Similar pitch-roll manoeuvres are also observed in hovering

male horse flies (Hybomitra hinei wrighti) while they rapidlychange direction to chase passing females or any small fast-movingobjects (Wilkerson and Butler, 1984), and these manoeuvres werepreviously compared with the ‘Immelmann turn’ commonly used inthe aerobatic manoeuvres of aircraft to rapidly reposition with180 deg heading change. Compared with banked yaw turns (Clark,2011; Muijres et al., 2015), which may create similar global yawturning angle and end forward velocity, a pitch-roll turn allows abird to almost instantly burst into backward flight to evade the startlestimulus (or creating larger backward acceleration at the start of themanoeuvre; also see Clark, 2011) and then smoothly transition toforward flight by rolling its body. It also ensures a nearly continuousacceleration towards the direction of escape, but it should requireaccurate control or preplanning of the timing of roll rotation (Chenget al., 2016). This interpretation assumes near-maximal flightperformance, which is reasonable because the hummingbirdsremained vigilant during the experiments. Nonetheless, given thevagaries of motivation possible for wild animals subjected to

repeated tests in captivity, caution is warranted in interpreting ourconclusion of optimality.

Interspecific differences of body kinematicsAlthough four hummingbird species showed stereotyped pitch-rollmanoeuvres in response to the startling stimuli, two larger speciesperformed pitch rotations with considerably larger magnitude thansmaller species and attained larger global-yaw turns (Fig. 4).Comparing body kinematics of magnificent and black-chinnedhummingbirds (Fig. 3), cumulative body pitch angle was greater(Fig. 3E,M) and timing of roll rotation was noticeably later inmagnificent hummingbirds. However, peak roll rates (Fig. 3D,L)and cumulative roll angles (Fig. 3E,M) were similarinterspecifically. As a result, magnificent hummingbirdsperformed more drastic escape manoeuvres with larger global-yaw turn (Fig. 3C,K) and higher linear exiting velocities towards theend of manoeuvres (Fig. 3B,J).

Escape reaction timeTime lag between startling stimulus and tail flaring, which precededany noticeable changes of wing motion, were less in larger speciescompared with the smaller species. Reaction times were 21±1.4 msfor magnificent hummingbirds, 22.5±8.3 ms for blue-throatedhummingbirds, 28.5±8.1 ms for black-chinned hummingbirds and53.5±10.7 ms for broad-billed hummingbirds. Except for broad-billed hummingbirds, all the birds had reaction times much lowerthan those reported for the visual feedback of insects. For example,hawkmoths have >50 ms delays in responding to moving flowers(Sprayberry, 2009), and fruit flies have∼100 ms and∼61 ms delaysin responding to gust perturbation and looming-startling stimuli,respectively (Fuller et al., 2014; Muijres et al., 2014). These datareveal that hummingbirds are capable of faster visual processingthan insects. The estimated time delays here were comparable tothose reported for mechanosensory feedbacks of fruit flies: ∼20 msin wind sensing (Fuller et al., 2014), 10–25 ms in responding to yawperturbation (Ristroph et al., 2010) and 10–15 ms in responding topitch perturbation (Ristroph et al., 2013).

Wing kinematics of hoveringKinematic patterns of the distal wing of hovering hummingbirds,normalized by wingbeat frequency, show virtually no interspecific

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Fig. 4. The relationships between global yaw turning angle and three types of cumulative body rotation angles. (A) Cumulative body pitch angleprior to the start of roll rotation (

Ð trt0q � dt), which reflects the instantaneous pitch angle at the start of roll rotation or the timing of roll rotation relative the pitch

rotation; (B) total cumulative body pitch angle of the entire manoeuvre (Ð tft0q � dt), which reflects the magnitude of the pitch rotation; and (C) total cumulative body

roll angle (Ð tft0p � dt), which reflects the magnitude of the roll rotation. The cumulative body angles are different from the body Euler angles as they were integrated

directly from the body angular velocities. Results of the four species are shown in different colours. Linear regressions (dotted lines) show that global yaw headingchanges have strong correlations with the timing of roll rotation relative to the pitch rotation (A) and the magnitude of pitch rotation (B), but not with the magnitudeof the roll rotation (C).

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differences in time series (Fig. 5A–C) or wing-tip trajectories(Fig. 6). The shallow U-shaped tip trajectories were similar tothose measured from insects such as fruit flies (Muijres et al.,2014), drone flies (Liu and Sun, 2008) and hawkmoths (Chenget al., 2011).Comparing the kinematics derived from the distal wing planes

with those derived from the proximal planes (Fig. 5D–G)revealed substantial differences in the wing rotation angles(Fig. 5E). The distal and proximal wing planes had similar wingstroke and deviation angles, with the proximal section slightlyleading the distal section (Fig. 5D); however, there were largediscrepancies of wing rotation angle, especially during theupstroke. Thus the wings underwent large spanwise twist butonly minor spanwise bending when flapping. Previous studies ofhovering hummingbirds (Song et al., 2014; Warrick et al., 2005)have revealed that wing deformations included both chordwisecamber and spanwise twist. The time course of the twist rate ispresented in Fig. 5H, which shows that the spanwise twist wasmuch more substantial in the upstroke than in the downstroke.Although the magnitudes of wing pronation (in downstroke) andsupination (in upstroke) were similar at the distal section (blackcurve, Fig. 5E), at the proximal section, because of the wingtwist, there was much smaller supination than pronation (greencurve, Fig. 5E,G). This pattern of wing twist is similar to the‘washout’ design used in the blades of propellers and helicopters,which is implemented to reduce the induced-power loss in thewake and therefore increase the aerodynamic efficiency(Leishman, 2006).

Wing kinematics of escape manoeuvreWing kinematics derived from the distal wing plane showed greaterchanges from the hovering kinematics than those derived from theproximal plane and, therefore, were better indicators of activechanges of wing kinematics for controlling escape manoeuvres.These patterns are novel information for hummingbirds; incomparison with insects, whose wing kinematics during varioustypes manoeuvres are available from previous work (Beatus et al.,2015; Cheng et al., 2011; Fry et al., 2003; Muijres et al., 2014;Ristroph et al., 2010; Taylor, 2001). It has been observed thathummingbirds are able to rapidly generate substantial changes oftheir wing motion for manoeuvring. The manoeuvring wingkinematics show high temporal and spatial variability within eachhummingbird. The spatial variability is shown by the substantialchanges of wing motion in all three degrees of freedom, leading topronounced bilateral symmetric and asymmetric control of wingmotion. The temporal variability is shown by the rapid transitionbetween different wing kinematic patterns in different phases of themanoeuvre, which signifies the hummingbirds’ ability to quicklychange flight control force. As will be described further, below,compared with insects of smaller size, such as fruit flies, such anability of controlling the motion is required for hummingbirdsto generate comparable body angular rates. Arguably, this abilitycan be made possible for hummingbirds by their powerful flightmuscles for both up and down strokes (Tobalske et al., 2010),larger degrees of freedom provided by the proximal forelimbskeletomuscular system (Hedrick et al., 2011; Welch and Altshuler,2009), and the complex avian nervous system (Scanes, 2014). A

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Fig. 5. Wing kinematics in hoveringhummingbirds. (A–C) Wing kinematicangles derived from the distal wing plane forthe four species: (A) stroke, (B) rotation and(C) deviation. (D–F) Comparison of the wingkinematic angles derived from the distal andproximal wing planes (from blue-throatedhummingbird). The shaded areas enclosingthe curves indicate ±1 s.d. (N=4).(G) Schematic representation of the wingkinematics derived from the proximal anddistal wing planes. The line denotes thewingchord, with a circle marking the leadingedge. (H) Root rotation angle ψ0 (dotted line)and twist rate ψtw (solid line) as defined inEqn 4.

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complete summary of body and wing kinematic time series from anexample escape manoeuvre can be found in Fig. S1.Correlating mean wing kinematics with body movement, we

observed significant trends intraspecifically, but only a fewcorrelations were significant interspecifically (Tables S1–S4).Salient wing kinematic changes in all four species were apparentin wing-tip trajectories (Fig. 6) and were consistent with theinterspecifically-significant correlations. Wing kinematics werecorrelated primarily with the body angular velocities instead ofaccelerations, consistent with previous studies on avoidancemanoeuvres in hawkmoths (Cheng et al., 2011). This was at leastpartly due to the use of wing stroke-averaged kinematic variables, asany within-wingbeat acceleration and deceleration will cancel.Bilateral-symmetric changes were correlated with pitch andbilateral-asymmetric changes were correlated with roll and yaw(Table S1).The size of the flight chamber may have affected the performance

of escape manoeuvres compared with previous studies in largerarenas (Clark, 2011; Segre et al., 2015). The birds of different sizeswere able to complete a sequence of stereotyped body rotations andachieve comparable forward velocity at the end of the manoeuvres;however, they started to decelerate within two wingbeats aftercompleting their body rotations. In previous studies, the birdscontinued flying forward (Clark, 2011; Segre et al., 2015).Although the size of the chamber did not affect the completion ofthe escape manoeuvres, it may have increased the propensity to useof a particular type of manoeuvre, namely pitch-roll manoeuvrescompared with roll/yaw manoeuvres (Clark, 2011) and arcing turns(Segre et al., 2015), both of which require larger space for both fore/aft and lateral translation.

Wing kinematics for pitch rotationIn the beginning of an escape manoeuvre, hummingbirds rapidlypitched up and accelerated backwards; this was achieved byemploying bilateral–symmetric wing kinematic changes including:a backward tilt of stroke plane, a backward shift in mean spanwiserotation angle and a slight forward shift of mean stroke angle(Fig. 6). These kinematic changes were also accompanied by anincrease of wingbeat frequency and speed. There was a significantcorrelation between the above-wing kinematic variables and thestroke-averaged pitch rate (Fig. 7). The manoeuvring forces andmoments resulted from these kinematic changes can be inferredwithout detailed calculation of aerodynamic forces. Specifically, thebackward tilt of stroke plane oriented the mean lift force backward,creating lift-based pitch-up moment and backward force; thebackward shift of mean spanwise rotation angle (reducedpronation and enhanced supination) led to a higher angle of attackand drag during the downstroke, and a lower angle of attack and dragduring upstroke, thus creating drag-based pitch-up moment andbackward force; and the forward shift of mean stroke plane angle ledto an imbalance of lift with respect to the centre of mass, thuscreating a lift-based pitch moment without creating much backwardforce. Collectively, it can be seen that the hummingbirds exploitedall the major kinematic changes possible for generating pitchmoment and backward forces.

During escape manoeuvres, hummingbirds significantlyincreased their wingbeat frequencies (e.g. indicated by thereduced width of shaded areas in Fig. 2C,D,G,H). Larger speciesincreased their frequency by approximately 50% relative tohovering. Such drastic increases in wingbeat frequency were notobserved in previous maximal load-lifting experiments in the

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Fig. 6. Wing kinematics inmanoeuvring hummingbirds. The kinematics for the four species are shown in four separate panels: (A) magnificent hummingbird,(B) blue-throated hummingbird, (C) black-chinned hummingbird and (D) broad-billed hummingbird. In each panel, schematic representation of the wingkinematics during pitch and roll rotation are shown on the left and the corresponding time series of stroke, rotation and deviation angles are shown on the right.Colours are used to represent different wing kinematic patterns: black for wing kinematics during pitch, grey for hovering wing kinematics, and blue and red for left(inner) and right (outer) wing kinematics during roll. The shaded areas enclosing the curves indicate ±1 s.d. (N=4).

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hovering hummingbirds carrying weights (Chai et al., 1997) or withprogressively reduced air density (Chai and Dudley, 1995).However, in display dives, male black-chinned hummingbirdsalmost doubled their wingbeat frequency (reached 93 Hz) (Feo andClark, 2010). In load lifting, hummingbirds rely primarily onincreased stroke amplitude to augment lift (Chai et al., 1997; Chaiand Dudley, 1995). A major difference between the load-liftingexperiment and the present experiment was that the former usuallylasted longer periods of time, as the birds were required to take offby overcoming gravity and then sustain hovering for approximately1 s, while the duration of escape manoeuvres in our study was∼0.15 s. At least within the few wingbeats for generating highermanoeuvring forces and moments, the hummingbirds in our studyappeared capable of boosting muscle mass-specific power to asubstantially higher level than previously observed (Cheng et al.,2016).

Wing kinematics for roll rotationIn the second half of escape manoeuvres, a rapid body roll wascritical for reorientation of flight direction and recovery to stableforward or hovering flight. This was achieved by the bilateral–asymmetric wing kinematic changes in wing deviation, spanwise

rotation and velocity (roll pattern, Fig. 6, Table S3), all of which hadsignificant correlations with the body roll rates (Fig. 8). A bilateraldifference in wing deviation was conspicuous among these changes,especially for larger species (Fig. 6A,B). A bird elevated the outerwing and lowered the inner wing so that the normal axis of the strokeplane (xs) was tilted laterally towards the inner wing, or in thedirection of rolling. Similar to the stroke plane tilt in the pitchrotation, such a bilateral difference of wing motion likely created alift-based roll moment and a lateral force directed from the outerwing to the inner wing. Note that lateral force may be used forweight support to prevent any significant altitude loss when thebody is oriented horizontally with one side down (e.g. posture 6 inFig. 2B). Similar bilateral–asymmetric changes in the wingdeviation and stroke plane angle have been observed insignificantly slower yaw turns in Anna’s hummingbirds (Calypteanna) as they fed continuously from a revolving artificial feeder(Altshuler et al., 2012; Read et al., 2016).

Bilateral differences of wing spanwise rotation corresponded toreduced pronation and enhanced supination for the inner wing sothat its stroke-averaged lift was reoriented backwards and was moreperpendicular to the body longitudinal axis. Conversely, stroke-averaged lift of the outer wing was tilted forward and was more

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Fig. 7. The relationships between stroke-averaged pitch rates and the changes of wing kinematics. (i) Results for large species: blue-throated (blue) andmagnificent (red) hummingbirds. (ii) Results for small species: black-chinned (black) and broad-billed (green) hummingbirds. Stroke-averaged pitch rate asfunctions of (A) bilateral–symmetric change in wing spanwise rotation (ψl+ψr)/2, (B) bilateral–symmetric change in wing velocity (Ul+Ur)/2 and (C) bilateral–symmetric change in stroke plane angle (γl+γr)/2. The subscripts l and r denote left and right wings, respectively. Dotted lines represent the best-fit of the datathrough linear regression. The Pearson’s linear correlation coefficient and P-value (double-tail Student’s t distribution) between each pair of pitch rates and wingkinematic changes are shown at the bottom of each graph.

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parallel to the body longitudinal axis. This asymmetry likely createda lift-based roll moment as well as a coupled yaw moment. Finally,the bilateral difference of wing stroke amplitude (Fig. 6) and,correspondingly, the wing velocity led to an imbalance of liftbetween the inner and outer wings, and therefore also created a lift-based roll moment. Bilateral–asymmetric changes in thewing strokeamplitude were also observed by Altshuler et al. (2012).Roll moment was mostly created during the downstrokes, when

total force was mostly perpendicular to the body longitudinal axis;during the upstroke, the total force was approximately parallel to thelongitudinal body axis, and was thus less effective in creating rollmoment, but more effective in creating yaw moment; thisinterpretation is confirmed through aerodynamic analysis (Chenget al., 2016). Statistical analysis shows that for all four species, onlydownstroke-averaged wing kinematic variables have significantcorrelations with roll rates (Tables S1, S3).

Wing kinematics for yaw rotationEscape manoeuvres were mainly composed of large pitch and rollrotations, and yaw rotation was less conspicuous. However, a minor(positive) yaw rotation during the initial pitching phase assisted thealignment of the body longitudinal axis to the direction of escape(Fig. 2D,H, 3D,J). For larger species (Figs 2D, 3D), we also foundthat, in addition to the dominant roll rotation, a (negative) yawrotation helped to reorient the body back to a normal hovering orforward flight posture. Yaw moment was mainly created in theupstroke from bilateral differences in wing spanwise rotation, whichwere also concurrent with roll moment. There was significant

correlation between the yaw rate and the bilateral difference of wingspanwise rotation averaged over the upstroke but not over thedownstroke (Table S4).

Wing kinematic variables averaged over the downstrokes hadmore-significant correlations with the body kinematics than thoseaveraged over the upstrokes (except for yaw), thus revealing thecrucial role of downstroke in the control of escape manoeuvres(Warrick et al., 2005, 2009); this is further confirmed throughaerodynamic analysis (Cheng et al., 2016). This result is alsoconsistent with the twofold difference in muscle mass betweenpectoralis major and supracoracoideus in hummingbirds (Hartman,1961).

DISCUSSIONComparing the manoeuvres of fruit flies and hummingbirdsDespite differences in size and biological design, escapemanoeuvres of hummingbirds in response to looming stimuluswere similar to those of fruit flies in terms of peak roll and pitch rates(Muijres et al., 2014) and peak angular rates during voluntary yawmanoeuvres (Hedrick et al., 2009). The similar rotationalmanoeuvrability between these two taxa is a result of complexinteractions of neural, physiological and dynamic processes thatwere independently shaped by evolutionary and ecologicaldemands. However, wing manoeuvring kinematics of these twotaxa show that the underlying dynamics, without considering theneural and physiological processes, are quite different.Hummingbirds used greater changes of wing kinematics than fruitflies; this was mainly due to the broad scaling effect that favours

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Fig. 8. The relationships between stroke-averaged roll rates and the changes of wingkinematics. (i) Results for large species: blue-throated (blue) and magnificent (red)hummingbirds. (ii) Results for small species: black-chinned (black) and broad-billed (green)hummingbirds. Stroke-averaged roll rate asfunctions of (A) bilateral difference in wingdeviation (θl–θr) and (B) bilateral difference in wingspanwise rotation (ψl–ψr). Other definitions are asin Fig. 7.

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smaller fliers, allowing them to generate higher angular velocity andacceleration than their larger counterparts (Kumar and Michael,2012). This is also apparent in power expenditures of larger andsmaller hummingbirds (Cheng et al., 2016). For animals as small asfruit flies, if they were to use similar amounts of change in wingkinematics as hummingbirds, the accelerations generated wouldquickly destabilize their flight, and their sensorimotor system maynot respond rapidly enough to ensure a stable flight (Chang andWang, 2014). Fruit flies only use subtle wing kinematic changes infree-flight manoeuvres (Bergou et al., 2010; Fry et al., 2003;Muijres et al., 2015) except when being forced into extreme flightconditions with significantly higher body rates than those found inthe free-flight manoeuvres (Beatus et al., 2015).Although subtle wing kinematic changes are sufficient for

generating rotational moments in fruit flies, this may limit theirability to change the directions of aerodynamic forces. Even duringthe fastest escape manoeuvres, the total aerodynamic force vector ofa fruit fly changes very little relative to the body, such that a‘helicopter model’ is a valid descriptor (Muijres et al., 2015). Forhummingbirds, large changes in wing kinematic angles indicate thatthey modulate force vectors relative to their body, and, therefore, donot conform to the ‘helicopter model’. This is confirmed viaestimating the aerodynamic force vector based on the bodyacceleration and gravity, and then calculating its longitudinal(Fig. 3G,O) and lateral (Fig. 3H,P) tilt angles. From the plot, we cansee that there is a large backward tilt of force vector in the pitchingphase of the escape manoeuvre, at least 35 deg for the magnificenthummingbird and 60 deg for the black-chinned hummingbird. Thisis further confirmed via detailed aerodynamic force calculation(Cheng et al., 2016). As a result, hummingbirds may createmanoeuvring forces independent of their body angles and enjoyenhanced linear manoeuvrability compared with smaller animals.This could be a significant locomotive advantage for them whenpreying on insects.

Head saccadesThe start of body roll at the second half of manoeuvrewas concurrentwith a rapid head saccade towards the escape direction (Figs 2, 3).Head saccades lasted approximately 40–50 ms (Fig. 3F,N) with amagnitude close to 150 deg, and finished prior to the completion ofbody roll rotation (also see Fig. 2B,F). This corresponds to anaverage saccade rate higher than 3000 deg s−l, which is slightly fasterthan the peak head-saccade rate reported in lovebirds (Agapornisroseicollis) and significantly faster than those reported for othervertebrates (Kress et al., 2015). In the entire manoeuvre, except therapid-saccade phase, the head maintained a highly stable orientationwith respect to the global frame in spite of the body rotation,putatively owing to the bird’s vestibular system (Haque andDickman, 2005; Money and Correia, 1972). As a result, thestability of head orientation and the short duration of head saccademay contribute to attaining a stable gaze and reducing the period ofvisual blur, thereby enhancing visual feedback for high-levelplanning of the subsequent flight, for example, to stop and avoidrunning into the wall of the flight chamber. In contrast, because thehead saccade preceded completion of body roll, the roll control at thesecond half of the manoeuvre was unlikely to be regulated directlyby the visual feedback. Assuming stabilized head/vision, onehypothesis that merits further study is that the proprioception fromthe neck (Necker, 2001) was used to regulate the body roll angletowards the end of the manoeuvre (by afferent encoding of musclestrain between the head and the body). Although putative pathwaysare known (Necker, 2001), the function of such pathways in flight

has not been studied. An analogous pattern for proprioception forflight control is used in various insects with cuticular hairs located attheir prothorax that detect head angle, including dragonflies(Mittelstaedt, 1950), bluebottle flies (Liske, 1977) and locusts(Taylor, 1981).

AcknowledgementsWe thank the director and staff at the Southwestern Research Station (under thedirection of the AmericanMuseumof Natural History, NewYork, USA) for hosting ourresearch efforts; Joana Figuie re, Kathleen Langland, Rebecca Schroeder andJoseph Canepa for assisting with bird capture; Yi Wang and Stephen Van Kooten forassisting in extraction of wing kinematics and drawing some schematic figures; andtwo anonymous reviewers for providing insightful suggestions that helped usimprove the quality of the manuscript.

Competing interestsThe authors declare no competing or financial interests.

Author contributionsB.C., B.W.T., G.T.C.C. and X.D. contributed to the design of experiments, B.C.,B.W.T., D.R.P. and S.M.W. prepared the experiments, and B.C. and B.W.T.performed the experiments. All authors contributed to the interpretation of findingsand preparation of the manuscript, and B.C., B.W.T. and T.L.H. contributed to thedata analysis.

FundingFunding was provided by the National Science Foundation [NSF CMMI 1234737 toX.D., B.W.T. and T.L.H.] and the National Aeronautics and Space Administration[Climate and Biological Response 10-BIOCLIM10–0094 to D.R.P.].

Supplementary informationSupplementary information available online athttp://jeb.biologists.org/lookup/doi/10.1242/jeb.137539.supplemental

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